Entanglement scaling at first order phase transitions

First order quantum phase transitions (1QPTs) are signaled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations. When a 1QPT is crossed in the vicinity of a second order one (2QPT), due to the correlation length divergence of the latter, the corresponding ground state is modified and it becomes increasingly difficult to determine the order of the transition when the size of the system is finite. Here we show that, in such situations, it is possible to apply finite size scaling to entanglement measures, as it has recently been done for the order parameters and the energy gap, in order to recover the correct thermodynamic limit. Such a finite size scaling can unambigously discriminate between first and second order phase transitions in the vicinity of multricritical points even when the singularities displayed by entanglement measures lead to controversial results

Bound entanglement in the Jaynes-Cummings model

We study in detail entanglement properties of the Jaynes-Cummings model assuming a two-level atom (qubit) interacting with the first $N$ levels of an electromagnetic field mode (qudit) in a cavity. In the Jaynes-Cummings model, the number operator is the conserved quantity that allows for the exact diagonalization of the Hamiltonian and thus we study states that commute with this conserved quantity and whose structure is preserved under the Jaynes-Cummings dynamics. Contrary to the common belief, we show that there are bound entangled states that satisfy the symmetries imposed by the conservation of the number of excitations when $N>3$. Furthermore we show that \emph{the Jaynes-Cummings interaction can be used to generate bound-entanglement} between the atom and the mode.Comment: Improved abstract, references and new section on the generation of bound entanglement using the JC interactio

Optimal Ensemble Length of Mixed Separable States

The optimal (pure state) ensemble length of a separable state, A, is the minimum number of (pure) product states needed in convex combination to construct A. We study the set of all separable states with optimal (pure state) ensemble length equal to k or fewer. Lower bounds on k are found below which these sets have measure 0 in the set of separable states. In the bipartite case and the multiparticle case where one of the particles has significantly more quantum numbers than the rest, the lower bound for non-pure state ensembles is sharp. A consequence of our results is that for all two particle systems, except possibly those with a qubit or those with a nine dimensional Hilbert space, and for all systems with more than two particles the optimal pure state ensemble length for a randomly picked separable state is with probability 1 greater than the state's rank. In bipartite systems with probability 1 it is greater than 1/4 the rank raised to the 3/2 power and in a system with p qubits with probability 1 it is greater than (2^2p)/(1+2p), which is almost the square of the rank.Comment: 8 page

Nou mètode per detectar estats "exòtics" de la matèria condensada

El grup de computació quàntica de la UAB ha participat en una recerca internacional que proposa un mètode nou, superior als que existeixen fins ara, per detectar estats "exòtics" de la matèria condensada, de tal manera que la mostra (àtoms ultrafreds) no es destrueixi en ser observada. Aquest mètode s'ha anomenat Quantum non demolition, i és la mesura menys destructiva possible que permeten les lleis de la mecànica quàntica. Aquest treball, publicat a Nature, s'ha dut a terme en col·laboració amb l'Institut de Ciències Fotòniques (ICFO) i el Niels Bohr Institute de Dinamarca.El grupo de computación cuántica de la UAB ha liderado una investigación que propone un método nuevo, superior a los que existen hasta ahora, para detectar estados "exóticos" de la materia condensada de tal manera que la muestra (átomos ultrafríos) no se destruya al ser observada. Este método se ha llamado Quantum non demolition, y es la medida menos destructiva posible que permiten las leyes de la mecánica cuántica. Este trabajo, publicado en Nature, se ha llevado a cabo en colaboración con el Instituto de Ciencias Fotónicas (ICFO) y el Niels Bohr Institute de Dinamarca

Genuine quantum correlations in quantum many-body systems: a review of recent progress

Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.Comment: Review. Close to published version. Comments are welcome! Please write an email to g.dechiara[(at)]qub.ac.u